Computational methods for optical molecular imaging

• Published in: Communications in numerical methods in engineering Vol. 25; no. 12; pp. 1137 - 1161
• Main Authors: Chen, Duan, Wei, Guo-Wei, Cong, Wen-Xiang, Wang, Ge
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.12.2009; Wiley
• Subjects: Animals; Applied sciences; Artificial intelligence; Biological and medical sciences; computational techniques; Computer science; control theory; systems; Diffusion; Exact sciences and technology; Imaging; Investigative techniques, diagnostic techniques (general aspects); matched interface and boundary; Mathematical analysis; Mathematical models; Medical sciences; Miscellaneous. Technology; molecular imaging; optical diffusion equation; Organs; Pathology. Cytology. Biochemistry. Spectrometry. Miscellaneous investigative techniques; Pattern recognition. Digital image processing. Computational geometry; Photons; Singularities; tomography; Discontinuity; Singularity; Difference scheme; Complex shape; Biological tissues; Topology; Experimental study; molecular imaging; Modeling; optical diffusion equation; Geometrical model; Finite element method; matched interface and boundary; Animal; Optical properties; Tomography; Medical imagery; computational techniques; Diffusion equation; Robustness; Localization; Finite difference method
• ISSN: 1069-8299; 2040-7947; 2040-7939; 1099-0887; 2040-7947
• DOI: 10.1002/cnm.1164

A new computational technique, the matched interface and boundary (MIB) method, is presented to model the photon propagation in biological tissue for the optical molecular imaging. Optical properties have significant differences in different organs of small animals, resulting in discontinuous coefficients in the diffusion equation model. Complex organ shape of small animal induces singularities of the geometric model as well. The MIB method is designed as a dimension splitting approach to decompose a multidimensional interface problem into one‐dimensional ones. The methodology simplifies the topological relation near an interface and is able to handle discontinuous coefficients and complex interfaces with geometric singularities. In the present MIB method, both the interface jump condition and the photon flux jump conditions are rigorously enforced at the interface location by using only the lowest‐order jump conditions. This solution near the interface is smoothly extended across the interface so that central finite difference schemes can be employed without the loss of accuracy. A wide range of numerical experiments are carried out to validate the proposed MIB method. The second‐order convergence is maintained in all benchmark problems. The fourth‐order convergence is also demonstrated for some three‐dimensional problems. The robustness of the proposed method over the variable strength of the linear term of the diffusion equation is also examined. The performance of the present approach is compared with that of the standard finite element method. The numerical study indicates that the proposed method is a potentially efficient and robust approach for the optical molecular imaging. Copyright © 2008 John Wiley & Sons, Ltd.